I've asked elsewhere but nobody knew it, and a search through the internet didn't turn up anything, either.

It's a song that was played on the "Midnight Special" radio program. It's a male singer accompanied on the guitar and the only words I remember are "When Paul was only six years old".

It's British and about a child who is treated badly by his parents. The humor comes from them treating him in a way which would be appropriate for an adult but cruel when applied to a child. For instance, when he tries to nurse, his mother pushes him away saying "cheeky beggar" or something similar.